Nonlinear four-wave interaction and freak waves

Four-wave interactions play an important role in the evolution of the spectrum of surface gravity waves. This follows from direct simulations of an ensemble of ocean waves using the Zakharov equation. The theory of homogeneous four-wave interactions, extended to include effects of nonresonant transfer, compares favourably with the ensemble averaged results of the Monte Carlo simulations. In particular, there is good agreement regarding spectral shape. Also, the kurtosis of the surface elevation probability distribution is well-determined by theory even for waves with a narrow spectrum and large steepness. These extreme conditions are favourable for the occurrence of freak waves and are well-described by the so-called Benjamin-Feir Index (BFI), which is essentially the ratio of the steepness of the waves and the width of the spectrum. In order to validate the theory, many occurrences of extreme wave events are required. Presently, this is only possible in the laboratory by performing wave tank experiments. Good agreement between observed and theoretical probability distribution functions is found. In October 2003 ECMWF introduced a new set of wave parameters, such as the BFI, which serve as an indicator for extreme events. Validation of such a Freak Wave Warning system is highly desirable.